5x(x-5)-52=4x(x-4)

Solution for 5x(x-5)-52=4x(x-4) equation:

5x(x-5)-52=4x(x-4)

We move all terms to the left:

5x(x-5)-52-(4x(x-4))=0

We multiply parentheses

5x^2-25x-(4x(x-4))-52=0


We calculate terms in parentheses: -(4x(x-4)), so:

4x(x-4)

We multiply parentheses

4x^2-16x

Back to the equation:

-(4x^2-16x)


We get rid of parentheses

5x^2-4x^2-25x+16x-52=0

We add all the numbers together, and all the variables

x^2-9x-52=0

a = 1; b = -9; c = -52;
Δ = b2-4ac
Δ = -92-4·1·(-52)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-17}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+17}{2*1}=\frac{26}{2}
=13
$